mlsanityData to 14 Oct 2026

Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems

arXiv 2301.10391 ↗First posted 25 Jan 2023cs.LG physics.comp-phcited by 14

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Abstract (arXiv)

We present a data-driven, space-time continuous framework to learn surrogate models for complex physical systems described by advection-dominated partial differential equations. Those systems have slow-decaying Kolmogorov n-width that hinders standard methods, including reduced order modeling, from producing high-fidelity simulations at low cost. In this work, we construct hypernetwork-based latent dynamical models directly on the parameter space of a compact representation network. We leverage the expressive power of the network and a specially designed consistency-inducing regularization to obtain latent trajectories that are both low-dimensional and smooth. These properties render our surrogate models highly efficient at inference time. We show the efficacy of our framework by learning models that generate accurate multi-step rollout predictions at much faster inference speed compared to competitors, for several challenging examples.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Builds on 29 of its 69 references that are in the map. First posted on arXiv 25 Jan 2023.

Builds on

29 of 69 references.

References · 29

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17 more
  1. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
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Citing papers per year: 2023: 4; 2024: 8; 2025: 1; 2026: 1.

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  1. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 109
  2. 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 91
  3. 2024DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systemscited by 30
  4. 2024CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equationscited by 14
  5. 2023Reduced-order modeling for parameterized PDEs via implicit neural representationscited by 8
  6. 2023Operator learning for hyperbolic partial differential equationscited by 5
  7. 2024Advancing Generalization in PINNs through Latent-Space Representationscited by 5
  8. 2024Physics-informed reduced order model with conditional neural fieldscited by 4
  9. 2024Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularizationcited by 3
  10. 2024The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantificationcited by 3
  11. 2025Uncertainty Quantification for Reduced-Order Surrogate Models Applied to Cloud Microphysicscited by 1
  12. 2026Learning Permutation-invariant Macroscopic Dynamicscited by 1
2 more
  1. 2023Attention-enhanced neural differential equations for physics-informed deep learning of ion transportcited by 0
  2. 2024Scalable physical source-to-field inference with hypernetworkscited by 0